Temperature and heat
- Temperature measures the average kinetic energy of the particles in a substance.
- Heat (Q) is thermal energy transferred from a hotter object to a cooler one.
- Thermal energy is the total kinetic and potential energy of all the particles.
A bathtub of warm water has more thermal energy than a cup of boiling water, even though the cup has a higher temperature, because the bathtub has many more particles.
Temperature scales: K = °C + 273.15. Absolute zero (0 K) is the lowest possible temperature.
Three ways heat moves
| Method | How it works | Examples |
|---|---|---|
| Conduction | Particles collide and pass energy to neighbours; needs contact | A metal spoon heating in soup; touching a hot pan |
| Convection | Warm fluid rises, cool fluid sinks, creating currents | Boiling water; sea breezes; ovens; mantle currents in Earth |
| Radiation | Electromagnetic waves (mostly infrared) carry energy; no medium needed | Sunlight warming Earth; heat from a campfire |
- Conductors (metals) transfer heat well because free electrons carry energy.
- Insulators (air, wool, foam, fibreglass) transfer heat poorly. Trapped air is an excellent insulator, which is why down jackets and double-paned windows work.
Dark, dull surfaces absorb and emit radiation well; shiny, light surfaces reflect it. That’s why emergency blankets are shiny.
A thermos reduces all three: a vacuum layer stops conduction and convection, and silvered walls reflect radiation.
Calculating heat
Q = mcΔT
- c = specific heat capacity (J/kg·°C or J/g·°C)
- Water: c = 4180 J/kg·°C
Phase changes need energy without changing temperature:
Q = mL
| Latent heat of water | Value |
|---|---|
| Fusion (melting/freezing) | 334 kJ/kg |
| Vaporization (boiling/condensing) | 2260 kJ/kg |
That’s why steam burns are worse than boiling-water burns: steam releases 2260 kJ/kg when it condenses on your skin.
Thermal equilibrium and the zeroth law
When two objects touch, heat flows from hot to cold until they reach the same temperature: thermal equilibrium.
Zeroth law of thermodynamics: if A is in equilibrium with B, and B with C, then A is in equilibrium with C. This is why thermometers work.
The first law of thermodynamics
ΔU = Q − W
- ΔU = change in internal energy
- Q = heat added to the system
- W = work done by the system
This is the law of conservation of energy applied to heat. You can’t get more energy out of a system than you put in.
Example: A gas absorbs 500 J of heat and does 200 J of work pushing a piston. ΔU = 500 − 200 = 300 J.
The second law of thermodynamics
The second law has several equivalent statements:
- Heat flows naturally from hot to cold, never the reverse without outside work.
- No heat engine can convert all its heat input into work; some must be released to a cold reservoir.
- The total entropy of an isolated system never decreases.
Entropy measures how spread out or disordered energy is. Ice melting, perfume spreading through a room and a hot drink cooling all increase entropy.
Heat engines
A heat engine takes heat Q_H from a hot source, does work W, and releases heat Q_C to a cold sink.
efficiency = W ÷ Q_H = 1 − Q_C ÷ Q_H
The maximum possible (Carnot) efficiency depends only on temperatures in kelvin:
e_max = 1 − T_C ÷ T_H
Example: An engine runs between 600 K and 300 K. e_max = 1 − 300/600 = 50%. Real engines achieve less.
Refrigerators and heat pumps run the cycle in reverse, using work to move heat from cold to hot. Heat pumps can deliver two to four times more heat energy than the electrical energy they use, which is why they’re increasingly used to heat homes in Canada.
The third law
The third law: it is impossible to reach absolute zero in a finite number of steps. Scientists have cooled atoms to within billionths of a kelvin, but never to exactly 0 K.
Common mistakes
- Confusing heat and temperature.
- Thinking cold flows into things. Heat flows out of warm things.
- Thinking a 100% efficient engine is possible.
- Using °C in the Carnot equation.
Try it yourself
- How much energy melts 0.5 kg of ice at 0 °C, then warms the water to 20 °C?
- Explain how a sea breeze forms during the day.
- A power plant burns fuel at 800 K and releases heat at 300 K. What is its maximum efficiency?
- Why does a metal bench feel colder than a wooden one at the same temperature?
(Answers: 167 kJ + 41.8 kJ ≈ 209 kJ; land heats faster, warm air rises, cooler sea air flows in; 62.5%; metal conducts heat away from your skin faster)
Quick recap
- Heat is energy transferred because of a temperature difference.
- Heat moves by conduction, convection and radiation.
- Q = mcΔT for temperature changes; Q = mL for phase changes.
- First law: ΔU = Q − W (energy conservation).
- Second law: entropy increases and no heat engine is 100% efficient.